Finite Group Databasebeta

← #16956358

Subgroups — #16956358

Order 4352.

1342 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762675C211yesmaximal, characteristic
2C2×C4×C4⋊Dic17C211yesmaximal, characteristic
3#14527052C212yesmaximal
4#14527046C212yesmaximal
5#14527016C212yesmaximal
6#14527014C211yesmaximal, characteristic
7#14527014C211yesmaximal, characteristic
8#14527014C211yesmaximal, characteristic
9#14527014C211yesmaximal, characteristic
10#14527009C212yesmaximal
11C2×C4×C4⋊C4×C17C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C4⋊Dic17C2211yescharacteristic
16C22×C4×Dic17C2212yes—
17#11762675—24no—
18C4×C4⋊Dic17—24no—
19C2×#10587502C2212yes—
20C2×#10587502C2212yes—
21C2×#10587502C2212yes—
22C2×#10587502C2212yes—
23C2×#10587502C2212yes—
24C2×#10587502C2212yes—
25C2×#10587502C2212yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C22×C4⋊C4×C17C2211yescharacteristic
31C22×C4⋊C4×C17C2211yescharacteristic
32C22×C42×C17C2211yescharacteristic
33C22×C42×C17C2211yescharacteristic
34C22×C42×C17C2211yescharacteristic
35C4×C4⋊C4×C17C418yescomplemented
36C2×C17×#95C2211yescharacteristic
37C2×C17×#95C2211yescharacteristic
38C23×C4×C17C2311yescharacteristic
39C23×C4×C17C2311yescharacteristic
40C23×C4×C17C2311yescharacteristic
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2311yescharacteristic
44C23×C4×C17C2311yescharacteristic
45C23×Dic17C2312yes—
46C23×Dic17C2312yes—
47C23×Dic17C2312yes—
48C23×Dic17C2312yes—
49C2×C4⋊C4×C17—22no—
50C2×C4⋊C4×C17—22no—
51C2×C4⋊C4×C17—22no—
52C2×C4⋊C4×C17—22no—
53C2×C4⋊C4×C17C2×C414yes—
54C2×C4⋊C4×C17C2×C414yes—
55C2×C42×C17—22no—
56C2×C42×C17—22no—
57C2×C42×C17—22no—
58C2×C42×C17—22no—
59C2×C42×C17—22no—
60C2×C42×C17—22no—
61C2×C42×C17C2×C414yes—
62C2×C42×C17C2×C414yes—
63C2×C42×C17C2×C414yes—
64C2×C4⋊Dic17—22no—
65C2×C4⋊Dic17—22no—
66C2×C4⋊Dic17—22no—
67C2×C4⋊Dic17—22no—
68C2×C4⋊Dic17—22no—
69C2×C4⋊Dic17—22no—
70C2×C4⋊Dic17—22no—
71C2×C4⋊Dic17—22no—
72C2×C4⋊Dic17—22no—
73C2×C4⋊Dic17—22no—
74C2×C4⋊Dic17D414yes—
75C2×C4⋊Dic17Q814yes—
76C2×C4×Dic17—24no—
77C2×C4×Dic17—24no—
78C2×C4×Dic17—42no—
79C17×#95C2×C414yes—
80C17×#95C2×C414yes—
81#10587502—24no—
82#10587502—24no—
83#10587502—24no—
84#10587502—24no—
85#10587502—24no—
86#10587502—24no—
87#10587502—42no—
88#10587502—42no—
89#10587502—42no—
90#10587502—42no—
91#10587502—42no—
92C24×C17C2411yescharacteristic
93C22×C4×C17—21no—
94C22×C4×C17—21no—
95C22×C4×C17—21no—
96C22×C4×C17—21no—
97C22×C4×C17—21no—
98C22×C4×C17—21no—
99C22×C4×C17—21no—
100C22×C4×C17—21no—
101C22×C4×C17—21no—
102C22×C4×C17—21no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—21no—
111C22×C4×C17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—21no—
114C22×C4×C17—21no—
115C22×C4×C17—21no—
116C22×C4×C17—21no—
117C22×C4×C17—21no—
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17C22×C412yes—
126C22×C4×C17C22×C412yes—
127C22×C4×C17C22×C412yes—
128C22×C4×C17C22×C412yes—
129C22×C4×C17C22×C412yes—
130C22×C4×C17C22×C412yes—
131C22×C4×C17C22×C412yes—
132C22×C4×C17C2×D412yes—
133C22×C4×C17C2×Q812yes—
134C22×C4×C17#4112yes—
135C22×C4×C17#4112yes—
136C22×C4×C17#4112yes—
137C22×C4×C17#4112yes—
138C22×C4×C17#4112yes—
139C22×C4×C17#4112yes—
140C22×C4×C17#4112yes—
141C22×C4×C17#4112yes—
142C22×Dic17—22no—
143C22×Dic17—22no—
144C22×Dic17—22no—
145C22×Dic17—22no—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17—22no—
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—22no—
160C22×Dic17—22no—
161C22×Dic17—22no—
162C22×Dic17—22no—
163C22×Dic17—22no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17C2×D414yes—
169C22×Dic17C2×Q814yes—
170C4⋊C4×C17—28no—
171C4⋊C4×C17—28no—
172C42×C17—28no—
173C42×C17—28no—
174C42×C17—28no—
175C4⋊Dic17—28no—
176C4⋊Dic17—28no—
177C4⋊Dic17—44no—
178C4⋊Dic17—44no—
179C4×Dic17—48no—
180#13885—171nomaximal, Sylow
181C23×C17C23×C411yescharacteristic
182C23×C17C22×D411yescharacteristic
183C23×C17C22×Q811yescharacteristic
184C23×C17C2×#4111yescharacteristic
185C23×C17C2×#4111yescharacteristic
186C23×C17C2×#4111yescharacteristic
187C23×C17C2×#4111yescharacteristic
188C23×C17C2×#4111yescharacteristic
189C23×C17C2×#4111yescharacteristic
190C23×C17C2×#4111yescharacteristic
191C23×C17C2×#4111yescharacteristic
192C23×C17H(5,𝔽2)11yescharacteristic
193C23×C17H(5,𝔽2)11yescharacteristic
194C23×C172−1+411yescharacteristic
195C23×C172−1+411yescharacteristic
196C2×C4×C17—22no—
197C2×C4×C17—22no—
198C2×C4×C17—22no—
199C2×C4×C17—22no—
200C2×C4×C17—22no—
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—22no—
206C2×C4×C17—22no—
207C2×C4×C17—22no—
208C2×C4×C17—22no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17—22no—
212C2×C4×C17—22no—
213C2×C4×C17—22no—
214C2×C4×C17—22no—
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—22no—
218C2×C4×C17—22no—
219C2×C4×C17—22no—
220C2×C4×C17—41no—
221C2×C4×C17—41no—
222C2×C4×C17—41no—
223C2×C4×C17—41no—
224C2×C4×C17—41no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17—41no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
233C2×C4×C17—41no—
234C2×C4×C17—41no—
235C2×C4×C17—41no—
236C2×C4×C17#11714yes—
237C2×C4×C17#11714yes—
238C2×C4×C17#11714yes—
239C2×C4×C17C4×D414yes—
240C2×C4×C17C4×Q814yes—
241C2×C4×C17C22⋊Q814yes—
242C2×C4×C17#12314yes—
243C2×C4×C17#12514yes—
244C2×C4×C17#12614yes—
245C2×Dic17—24no—
246C2×Dic17—24no—
247C2×Dic17—24no—
248C2×Dic17—24no—
249C2×Dic17—24no—
250C2×Dic17—24no—
251C2×Dic17—42no—
252C2×Dic17—42no—
253C2×Dic17—42no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—42no—
259C2×Dic17—42no—
260C2×Dic17—42no—
261C2×Dic17—42no—
262C2×Dic17—42no—
263C2×Dic17—42no—
264C2×Dic17—42no—
265C2×Dic17—42no—
266C2×Dic17—42no—
267C2×Dic17—42no—
268C2×Dic17—42no—
269C2×Dic17—42no—
270C2×Dic17—42no—
271C2×Dic17—42no—
272C2×Dic17—42no—
273C2×#382—171no—
274C2×C4×C4⋊C4—171no—
275C2×C4×C4⋊C4D1711yescharacteristic
276#1445—172no—
277#1443—172no—
278#1436—172no—
279C4⋊#95—171no—
280C4⋊#95—171no—
281C4⋊#95—171no—
282C4⋊#95—171no—
283#1434—172no—
284C22×C17C2×#11711yescharacteristic
285C22×C17C2×#11711yescharacteristic
286C22×C17C2×#11711yescharacteristic
287C22×C17C2×C4×D411yescharacteristic
288C22×C17C2×C4×Q811yescharacteristic
289C22×C17#52011yescharacteristic
290C22×C17#52011yescharacteristic
291C22×C17C2×C22⋊Q811yescharacteristic
292C22×C17C2×#12311yescharacteristic
293C22×C17C2×#12511yescharacteristic
294C22×C17C2×#12611yescharacteristic
295C22×C17#52911yescharacteristic
296C22×C17#52911yescharacteristic
297C22×C17#52911yescharacteristic
298C22×C17#52911yescharacteristic
299C22×C17#54011yescharacteristic
300C22×C17#54111yescharacteristic
301C22×C17#54211yescharacteristic
302C22×C17#54211yescharacteristic
303C22×C17#54611yescharacteristic
304C22×C17#54711yescharacteristic
305C22×C17#54811yescharacteristic
306C22×C17#55011yescharacteristic
307C22×C17#55211yescharacteristic
308C22×C17#55311yescharacteristic
309C22×C17#55411yescharacteristic
310C22×C17#55411yescharacteristic
311C22×C17#55511yescharacteristic
312C22×C17#55611yescharacteristic
313C22×C17#55611yescharacteristic
314C22×C17#55611yescharacteristic
315C22×C17#55711yescharacteristic
316C22×C17#55711yescharacteristic
317C22×C17#55911yescharacteristic
318C22×C17#55911yescharacteristic
319C4×C17—24no—
320C4×C17—24no—
321C4×C17—42no—
322C4×C17—42no—
323C4×C17—42no—
324C4×C17—42no—
325C4×C17#38718yes—
326Dic17—44no—
327Dic17—44no—
328Dic17—82no—
329Dic17—82no—
330C22×C4⋊C4—171no—
331C22×C4⋊C4—171no—
332C22×C4⋊C4—171no—
333C22×C4⋊C4—171no—
334C22×C4⋊C4C2×D1711yescharacteristic
335C22×C4⋊C4C2×D1711yescharacteristic
336C22×C42—172no—
337C22×C42C2×D1711yescharacteristic
338C22×C42C2×D1711yescharacteristic
339C22×C42C2×D1711yescharacteristic
340#382—344no—
341C4×C4⋊C4—344no—
342C4×C4⋊C4Dic1718yescomplemented
343C2×#95—172no—
344C2×#95—172no—
345C2×#95—172no—
346C2×#95—172no—
347C2×#95—172no—
348C2×#95—172no—
349C2×#95—172no—
350C2×#95—172no—
351C2×#95—172no—
352C2×#95—172no—
353C2×#95—172no—
354C2×#95C2×D1711yescharacteristic
355C2×#95C2×D1711yescharacteristic
356C2×C17#228311yescharacteristic
357C2×C17C2×#38711yescharacteristic
358C2×C17#231411yescharacteristic
359C2×C17#235211yescharacteristic
360C2×C17#235411yescharacteristic
361C2×C17#235511yescharacteristic
362C2×C17#235511yescharacteristic
363C2×C17#244711yescharacteristic
364C2×C17#244811yescharacteristic
365C2×C17#245311yescharacteristic
366C2×C17#245411yescharacteristic
367C2×C17#250811yescharacteristic
368C2×C17#250911yescharacteristic
369C2×C17#251311yescharacteristic
370C2×C17#251411yescharacteristic
371C23×C4—172no—
372C23×C4—172no—
373C23×C4—172no—
374C23×C4—172no—
375C23×C4C22×D1711yescharacteristic
376C23×C4C22×D1711yescharacteristic
377C23×C4C22×D1711yescharacteristic
378C23×C4C22×D1711yescharacteristic
379C23×C4C22×D1711yescharacteristic
380C23×C4C22×D1711yescharacteristic
381C23×C4C22×D1711yescharacteristic
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—174no—
387C2×C4⋊C4—174no—
388C2×C4⋊C4—342no—
389C2×C4⋊C4—342no—
390C2×C4⋊C4—342no—
391C2×C4⋊C4—342no—
392C2×C4⋊C4—342no—
393C2×C4⋊C4—342no—
394C2×C4⋊C4—342no—
395C2×C4⋊C4—342no—
396C2×C4⋊C4—342no—
397C2×C4⋊C4—342no—
398C2×C4⋊C4C2×Dic1714yes—
399C2×C4⋊C4C2×Dic1714yes—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—344no—
407C2×C42—344no—
408C2×C42—682no—
409C2×C42C2×Dic1714yes—
410C2×C42C2×Dic1714yes—
411C2×C42C2×Dic1714yes—
412#95—344no—
413#95—344no—
414#95—344no—
415#95—344no—
416#95—344no—
417#95—344no—
418#95—682no—
419#95—682no—
420#95—682no—
421#95—682no—
422#95—682no—
423#95C2×Dic1714yes—
424#95C2×Dic1714yes—
425C17#1388511yescharacteristic, complemented, Sylow
426C24C23×D1711yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—174no—
460C22×C4—174no—
461C22×C4—342no—
462C22×C4—342no—
463C22×C4—342no—
464C22×C4—342no—
465C22×C4—342no—
466C22×C4—342no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—342no—
477C22×C4—342no—
478C22×C4—342no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—342no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—342no—
485C22×C4—342no—
486C22×C4—342no—
487C22×C4#6325212yes—
488C22×C4#6325212yes—
489C22×C4#6325212yes—
490C22×C4#6325212yes—
491C22×C4#6325212yes—
492C22×C4#6325212yes—
493C22×C4D4×D1712yes—
494C22×C4#6325412yes—
495C22×C4Q8×D1712yes—
496C22×C4#6325612yes—
497C22×C4C22×Dic1712yes—
498C22×C4C22×Dic1712yes—
499C22×C4C22×Dic1712yes—
500C22×C4C22×Dic1712yes—
501C22×C4C22×Dic1712yes—
502C22×C4C22×Dic1712yes—
503C22×C4C22×Dic1712yes—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—348no—
507C4⋊C4—348no—
508C4⋊C4—684no—
509C4⋊C4—684no—
510C42—28no—
511C42—28no—
512C42—28no—
513C42—688no—
514C23C2×#6325211yescharacteristic
515C23C2×#6325211yescharacteristic
516C23C2×#6325211yescharacteristic
517C23C2×#6325211yescharacteristic
518C23C2×#6325211yescharacteristic
519C23C2×#6325211yescharacteristic
520C23C2×D4×D1711yescharacteristic
521C23C2×#6325411yescharacteristic
522C23C2×Q8×D1711yescharacteristic
523C23C2×#6325611yescharacteristic
524C23#1058769611yescharacteristic
525C23#1058769611yescharacteristic
526C23#1058769711yescharacteristic
527C23#1058769711yescharacteristic
528C23C23×Dic1711yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—344no—
570C2×C4—344no—
571C2×C4—344no—
572C2×C4—344no—
573C2×C4—344no—
574C2×C4—344no—
575C2×C4—682no—
576C2×C4—682no—
577C2×C4—682no—
578C2×C4—682no—
579C2×C4—682no—
580C2×C4—682no—
581C2×C4—682no—
582C2×C4—682no—
583C2×C4—682no—
584C2×C4—682no—
585C2×C4—682no—
586C2×C4—682no—
587C2×C4—682no—
588C2×C4—682no—
589C2×C4—682no—
590C2×C4—682no—
591C2×C4—682no—
592C2×C4—682no—
593C2×C4—682no—
594C2×C4—682no—
595C2×C4—682no—
596C2×C4—682no—
597C2×C4#1058757514yes—
598C2×C4#1058758014yes—
599C2×C4#1058758214yes—
600C2×C4#1058758414yes—
601C2×C4#1058761214yes—
602C2×C4#1058761214yes—
603C2×C4#1058761214yes—
604C2×C4D4×Dic1714yes—
605C2×C4Q8×Dic1714yes—
606C22C2×#1058761211yescharacteristic
607C22C2×#1058761211yescharacteristic
608C22C2×#1058761211yescharacteristic
609C22C2×D4×Dic1711yescharacteristic
610C22C2×Q8×Dic1711yescharacteristic
611C22#1176329211yescharacteristic
612C22#1176329211yescharacteristic
613C22C2×#1058758211yescharacteristic
614C22C2×#1058758011yescharacteristic
615C22C2×#1058757511yescharacteristic
616C22C2×#1058758411yescharacteristic
617C22#1176334311yescharacteristic
618C22#1176334311yescharacteristic
619C22#1176334311yescharacteristic
620C22#1176334311yescharacteristic
621C22#1176341411yescharacteristic
622C22#1176342111yescharacteristic
623C22#1176343011yescharacteristic
624C22#1176343011yescharacteristic
625C22#1176345511yescharacteristic
626C22#1176346411yescharacteristic
627C22#1176346811yescharacteristic
628C22#1176348011yescharacteristic
629C22#1176349911yescharacteristic
630C22#1176350511yescharacteristic
631C22#1176351911yescharacteristic
632C22#1176351911yescharacteristic
633C22#1176352411yescharacteristic
634C22#1176352911yescharacteristic
635C22#1176353211yescharacteristic
636C22#1176353211yescharacteristic
637C22#1176353711yescharacteristic
638C22#1176353711yescharacteristic
639C22#1176354411yescharacteristic
640C22#1176354411yescharacteristic
641C4—24no—
642C4—24no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—684no—
648C4—684no—
649C4—1362no—
650C4—1362no—
651C4#1176269518yes—
652C2#1453118211yescharacteristic
653C2C2×#1176269511yescharacteristic
654C2#1453139311yescharacteristic
655C2#1453171311yescharacteristic
656C2#1453173311yescharacteristic
657C2#1453174111yescharacteristic
658C2#1453174111yescharacteristic
659C2#1453257111yescharacteristic
660C2#1453258211yescharacteristic
661C2#1453264511yescharacteristic
662C2#1453265611yescharacteristic
663C2#1453332211yescharacteristic
664C2#1453333311yescharacteristic
665C2#1453338111yescharacteristic
666C2#1453339211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C4×C4⋊C4×C17C2
socle, prime radical, cosocleC24×C17C24
hypercenterC2×C4×C4⋊C4D17
hypocenterC17#13885
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
35. C4×C4⋊C4×C17C4semidirect
342. C4×C4⋊C4Dic17semidirect
425. C17#13885semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117626752
C2×C4×C4⋊Dic172
#145270522
#145270462
#145270162
#145270142
#145270092
C2×C4×C4⋊C4×C172
#1388517